{"title":"Intermediate prizes in multi-dimensional contests","authors":"Aner Sela","doi":"10.1007/s11238-024-09992-w","DOIUrl":null,"url":null,"abstract":"<p>We study <i>n</i> symmetric agents engaged in simultaneous <i>k</i>-dimensional contests. We demonstrate that there is no symmetric pure-strategy equilibrium when there are a sufficient number of agents and a prize is awarded only if the agent wins all <i>k</i> sub-contests. Therefore, intermediate prizes (a prize for a win in a single sub-contest) are required for the existence of symmetric pure-strategy equilibrium. We characterize the symmetric equilibrium for either simultaneous or sequential two-dimensional contests and show that the agents’ expected effort increases with the value of the intermediate prizes, and that when there are more than two agents, the optimal total effort in both types of contests is the same.</p>","PeriodicalId":47535,"journal":{"name":"Theory and Decision","volume":"49 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory and Decision","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s11238-024-09992-w","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study n symmetric agents engaged in simultaneous k-dimensional contests. We demonstrate that there is no symmetric pure-strategy equilibrium when there are a sufficient number of agents and a prize is awarded only if the agent wins all k sub-contests. Therefore, intermediate prizes (a prize for a win in a single sub-contest) are required for the existence of symmetric pure-strategy equilibrium. We characterize the symmetric equilibrium for either simultaneous or sequential two-dimensional contests and show that the agents’ expected effort increases with the value of the intermediate prizes, and that when there are more than two agents, the optimal total effort in both types of contests is the same.
我们研究了同时参与 k 维竞赛的 n 个对称代理。我们证明，如果有足够多的代理，并且只有在代理赢得所有 k 个子竞赛时才会获得奖励，那么就不存在对称的纯策略均衡。因此，对称纯策略均衡的存在需要中间奖品（在单项子竞赛中获胜的奖品）。我们描述了同时进行或连续进行的二维竞赛的对称均衡，并证明了代理人的预期努力会随着中间奖品价值的增加而增加，而且当有两个以上代理人时，两种竞赛中的最优总努力是相同的。
期刊介绍：
The field of decision has been investigated from many sides. However, research programs relevant to decision making in psychology, management science, economics, the theory of games, statistics, operations research, artificial intelligence, cognitive science and analytical philosophy have remained separate. Theory and Decision is devoted to all aspects of decision making belonging to such programs, but addresses also possible cross-fertilizations between these disciplines which would represent effective advances in knowledge. The purpose of the journal is to let the engineering of choice gradually emerge both for individual and for collective decision making. Formalized treatments will be favoured, to the extent that they provide new insights into the issues raised and an appropriate modeling of the situation considered. Due to its growing importance, expermentation in decision making as well as its links to the cognitive sciences will be granted special attention by Theory and Decision.
Of particular interest are: Preference and belief modeling,
Experimental decision making under risk or under uncertainty,
Decision analysis, multicriteria decision modeling,
Game theory, negotiation theory, collective decision making, social choice,
Rationality, cognitive processes and interactive decision making,
Methodology of the decision sciences. Applications to various problems in management and organization science, economics and finance, computer-supported decision schemes, will be welcome as long as they bear on sufficiently general cases. Analysis of actual decision making processes are also relevant topics for the journal, whether pertaining to individual, collective or negotiatory approaches; to private decisions or public policies; to operations or to strategic choices.
Officially cited as: Theory Decis
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